Triangle Area Calculator
Calculate area using multiple methods
Triangle Diagram
How to Calculate Triangle Area
The area of a triangle can be calculated using several different methods depending on which measurements you know. Each method is equally valid and will give the same result for the same triangle.
Method 1: Base and Height
This is the most common method. The formula is: Area = ½ × base × height
The height must be perpendicular to the base. This method works for all triangle types.
Method 2: Heron's Formula
When you know all three sides, use Heron's formula:
- Calculate the semi-perimeter: s = (a + b + c) / 2
- Calculate area: Area = √[s(s-a)(s-b)(s-c)]
Method 3: SAS (Side-Angle-Side)
When you know two sides and the included angle: Area = ½ × a × b × sin(C)
This method is particularly useful when working with trigonometry problems.
Frequently Asked Questions
What is the easiest way to find triangle area?
The easiest method is using base × height ÷ 2, if you know the base and perpendicular height. If you only know the sides, use Heron's formula.
What is Heron's formula?
Heron's formula calculates area when you know all three sides. First find s = (a+b+c)/2, then Area = √[s(s-a)(s-b)(s-c)].
Can I find area with only angles?
No, you need at least one side measurement. Angles alone don't determine the size of a triangle, only its shape. You need at least one linear dimension.
What if I know two sides and a non-included angle?
This is the SSA case. You first need to solve for the third side or the included angle using the law of sines or cosines, then you can calculate the area.
Does the method I choose affect the result?
No, all methods give the same area for the same triangle. Choose the method based on which measurements you know.
What are the units for area?
Area is always in square units. If your sides are in meters, the area is in square meters. If sides are in feet, area is in square feet.
How do I find the height if I don't know it?
If you know all three sides, use Heron's formula. If you know two sides and an angle, use the SAS method. Or rearrange Area = ½bh to find h = 2A/b.
Why is the formula ½ × base × height?
A triangle is exactly half of a parallelogram with the same base and height. Since a parallelogram's area is base × height, a triangle's area is half that.